Theorem 2.4 (Theorem F, [1]}) 
Let \(f\)  be a homeomorphism of \(\mathbb {A}\)  which is isotopic to the identity and let \(\check{f}\)  be a lift of f to \(\mathbb {R}^2\) . We suppose that \(\check{f}\)  is fixed point free and that there exists a positively recurrent point \(z\)  such that \(\operatorname{Rot}_{\check{f}}(z)\)  is well defined and equal to 0. Then \(f\)  has a topological horseshoe.

